What are the divisors of 716?

1, 2, 4, 179, 358, 716

There is a total of 6 positive divisors.
The sum of these divisors is 1260.
The arithmetic mean is 210.

4 even divisors

2, 4, 358, 716

2 odd divisors

1, 179

How to compute the divisors of 716?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 716 by each of the numbers from 1 to 716 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

716 / 1 = 716 (the remainder is 0, so 1 is a divisor of 716)
716 / 2 = 358 (the remainder is 0, so 2 is a divisor of 716)
716 / 3 = 238.66666666667 (the remainder is 2, so 3 is not a divisor of 716)
...
716 / 715 = 1.0013986013986 (the remainder is 1, so 715 is not a divisor of 716)
716 / 716 = 1 (the remainder is 0, so 716 is a divisor of 716)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 716 (i.e. 26.758176320519). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

716 / 1 = 716 (the remainder is 0, so 1 and 716 are divisors of 716)
716 / 2 = 358 (the remainder is 0, so 2 and 358 are divisors of 716)
716 / 3 = 238.66666666667 (the remainder is 2, so 3 is not a divisor of 716)
...
716 / 25 = 28.64 (the remainder is 16, so 25 is not a divisor of 716)
716 / 26 = 27.538461538462 (the remainder is 14, so 26 is not a divisor of 716)